Question

1. in an isosceles triangle, if the base angles are each 45 degrees, what is the measure of the vertex angle? 180 degrees 45 degrees 90 degrees 60 degrees

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$.

Step2: Identify base angles

In an isosceles triangle, the two base angles are equal. Here, each base angle is $45^\circ$, so their sum is $45^\circ + 45^\circ = 90^\circ$.

Step3: Calculate vertex angle

Subtract the sum of base angles from $180^\circ$: $180^\circ - 90^\circ = 90^\circ$.

Answer:

90 degrees (corresponding option: the one with "90 degrees")